Introduction

Find the github and MSU graduate student data by navigating with the pane on the left. The github data includes 35 time series, each representing the number of issues collected on a repository per day. The MSU student data includes 92 time series, each representing the number of active graduate students in a department per term.

GitHub Issues

MSU Students

Dickey-Fuller Results

GitHub Issues

Repo ID Start Length (Days) Dickey-Fuller P-Value Unit Root
1 2017-03-06 1239 -3.65 0.03 No
2 2014-07-31 2188 -2.25 0.47 Yes
3 2013-11-22 2439 0.04 0.99 Yes
4 2017-07-25 1098 -2.58 0.33 Yes
5 2013-04-15 2660 -3.93 0.01 No
6 2014-03-10 2331 -6.78 0.01 No
7 2013-12-06 2425 0.44 0.99 Yes
8 2017-10-12 1019 -2.79 0.24 Yes
9 2015-04-24 1921 -0.92 0.95 Yes
10 2014-01-08 2392 -3.35 0.06 Yes
11 2012-02-28 3072 -2.9 0.2 Yes
12 2014-10-02 2125 -2.33 0.44 Yes
13 2013-07-04 2580 -3.64 0.03 No
14 2016-02-16 1623 -6.15 0.01 No
15 2011-09-22 3231 -1.79 0.67 Yes
16 2015-02-06 1998 -2.75 0.26 Yes
17 2017-02-25 1248 -3.06 0.13 Yes
18 2015-03-13 1963 -2.84 0.22 Yes
19 2015-12-11 1690 -1.86 0.64 Yes
20 2018-08-24 703 -2.7 0.28 Yes
21 2016-02-22 1617 -2.55 0.34 Yes
22 2016-12-07 1328 -2.18 0.5 Yes
23 2015-11-09 1722 -3.98 0.01 No
24 2015-04-17 1928 -2.16 0.51 Yes
25 2016-12-16 1319 -2.58 0.33 Yes
26 2014-12-29 2037 -0.76 0.97 Yes
27 2013-06-11 2603 -0.54 0.98 Yes
28 2019-01-15 559 -2.59 0.33 Yes
29 2015-03-10 1966 -1.89 0.63 Yes
30 2015-03-14 1962 -2.47 0.38 Yes
31 2016-05-16 1533 -1.88 0.63 Yes
32 2015-03-20 1956 -2.45 0.39 Yes
33 2011-05-03 3373 -4.7 0.01 No
34 2017-05-19 1165 -1.4 0.83 Yes
35 2018-06-18 770 -2.2 0.5 Yes
Note:
80% of series contain unit root

MSU Students

Degree ID Start Date Length of Series (Semesters) Dickey-Fuller Statistic P-Value Unit Root Present
1 fall-2009 32 -2.69 0.31 Yes
2 summer-1994 52 -3.02 0.16 Yes
3 summer-1994 66 -3.49 0.05 No
4 summer-1994 25 -3.94 0.03 No
5 summer-1994 78 -2.31 0.45 Yes
6 fall-1997 68 -2.51 0.37 Yes
7 summer-1994 79 -2.46 0.39 Yes
8 summer-2002 54 -3.63 0.04 No
9 summer-1994 78 -3.24 0.09 Yes
10 summer-1994 78 -2.99 0.17 Yes
11 summer-1994 78 -3.13 0.11 Yes
12 summer-2005 45 -3.06 0.15 Yes
13 fall-1996 71 -2.14 0.52 Yes
14 spring-1997 45 -2.91 0.21 Yes
15 spring-2013 22 -2.93 0.22 Yes
16 fall-2009 32 -3.59 0.05 No
17 fall-2009 32 -2.60 0.34 Yes
18 summer-1994 58 -2.18 0.50 Yes
19 spring-2003 52 -3.84 0.02 No
20 summer-1995 61 -3.93 0.02 No
21 summer-1994 78 -2.99 0.17 Yes
22 fall-2002 54 -2.50 0.37 Yes
23 summer-1994 48 -2.39 0.42 Yes
24 summer-1994 78 -2.28 0.46 Yes
25 summer-1994 78 -2.68 0.30 Yes
26 summer-2005 45 -2.50 0.38 Yes
27 summer-1994 25 -2.41 0.42 Yes
28 summer-1994 78 -2.81 0.25 Yes
29 fall-2005 44 -3.82 0.03 No
30 summer-1994 42 -2.96 0.20 Yes
31 summer-1994 78 -4.92 0.01 No
32 summer-1994 78 -3.05 0.15 Yes
33 spring-2001 58 -3.46 0.05 Yes
34 spring-2001 58 -3.77 0.03 No
35 summer-1994 49 -2.93 0.20 Yes
36 fall-2005 44 -6.15 0.01 No
37 summer-1994 78 -3.12 0.12 Yes
38 fall-2009 32 -2.84 0.25 Yes
39 summer-1994 70 -3.57 0.04 No
40 summer-1994 78 -2.72 0.28 Yes
41 summer-1994 78 -2.83 0.24 Yes
42 fall-1998 65 -1.82 0.65 Yes
43 summer-1994 78 -3.05 0.15 Yes
44 summer-1998 66 -3.22 0.09 Yes
45 summer-1994 78 -4.26 0.01 No
46 summer-1994 78 -3.25 0.09 Yes
47 summer-1994 78 -2.62 0.32 Yes
48 summer-1994 78 -2.40 0.41 Yes
49 summer-1994 78 -2.77 0.26 Yes
50 summer-1994 78 -3.16 0.10 Yes
51 summer-1999 64 -3.33 0.08 Yes
52 summer-1994 78 -2.42 0.40 Yes
53 summer-1994 25 -4.03 0.02 No
54 fall-2002 53 -2.94 0.20 Yes
55 summer-1994 35 -3.57 0.05 No
56 summer-1994 36 -4.32 0.01 No
57 summer-1994 78 -3.14 0.11 Yes
58 summer-1996 72 -4.11 0.01 No
59 summer-1994 25 -2.33 0.45 Yes
60 spring-2002 55 -2.14 0.52 Yes
61 summer-1994 25 -3.39 0.08 Yes
62 summer-1997 69 -3.29 0.08 Yes
63 summer-1994 78 -2.48 0.38 Yes
64 fall-1998 65 -2.59 0.34 Yes
65 summer-1994 78 -3.76 0.03 No
66 summer-1994 78 -2.18 0.50 Yes
67 spring-2002 55 -2.35 0.43 Yes
68 summer-1994 24 -2.87 0.24 Yes
69 fall-2007 38 -3.29 0.09 Yes
70 fall-1998 65 -2.51 0.37 Yes
71 summer-1994 78 -2.75 0.27 Yes
72 summer-1994 78 -2.71 0.28 Yes
73 fall-2002 53 -3.20 0.10 Yes
74 summer-1994 78 -3.07 0.14 Yes
75 summer-1994 78 -3.11 0.12 Yes
76 summer-1994 78 -2.88 0.22 Yes
77 fall-2007 38 -3.28 0.09 Yes
78 spring-2002 55 -3.04 0.15 Yes
79 fall-2002 53 -2.98 0.18 Yes
80 summer-2006 32 -3.84 0.03 No
81 summer-1994 78 -2.72 0.28 Yes
82 summer-2005 45 -2.88 0.22 Yes
83 fall-2010 29 -2.97 0.20 Yes
84 fall-2000 59 -3.37 0.07 Yes
85 summer-1994 78 -3.37 0.07 Yes
86 summer-1994 78 -2.39 0.42 Yes
87 summer-1994 36 -4.72 0.01 No
88 fall-2002 53 -3.23 0.09 Yes
89 summer-1994 78 -3.74 0.03 No
90 summer-1994 43 -3.69 0.04 No
91 spring-2002 55 -2.61 0.33 Yes
92 fall-2009 28 -2.98 0.20 Yes
Note:
77% of series contain unit root

Law of Long Leads

The GitHub empirical data exhibited the long of law leads (also known as the arc-sine law). This law states that random walks infrequently change lead. When two move over time, the greatest probability is that one will spend most periods at a greater value than the other. The theoretical distribution is displayed below.

x-axis = Time, y-axis = Probability of Spending n Periods in the Lead

x-axis = Time, y-axis = Probability of Spending n Periods in the Lead

Periods or time points are displayed on the \(x\)-axis, and the probability of spending \(n\) periods in the lead is displayed on the \(y\)-axis. The greatest probabilities occur over \(n\) = max/min. That is, a walk is most likely to spend all or no periods above (below) the other. The same distribution manifests in my GitHub data. After evaluating all bi-user comparisons, the probability of spending n periods in the lead is displayed below.